Optimization by quantum annealing: Lessons from simple cases

L Stella*, GE Santoro, E Tosatti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


We investigate the basic behavior and performance of simulated quantum annealing (QA) in comparison with classical annealing (CA). Three simple one-dimensional case study systems are considered: namely, a parabolic well, a double well, and a curved washboard. The time-dependent Schrodinger evolution in either real or imaginary time describing QA is contrasted with the Fokker-Planck evolution of CA. The asymptotic decrease of excess energy with annealing time is studied in each case, and the reasons for differences are examined and discussed. The Huse-Fisher classical power law of double-well CA is replaced with a different power law in QA. The multiwell washboard problem studied in CA by Shinomoto and Kabashima and leading classically to a logarithmic annealing even in the absence of disorder turns to a power-law behavior when annealed with QA. The crucial role of disorder and localization is briefly discussed.

Original languageEnglish
Article number014303
Number of pages15
JournalPhysical Review B (Condensed Matter)
Issue number1
Publication statusPublished - Jul 2005


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